Probability and Measure

Wiley Series in Probability and Mathematical Statistics

by Patrick Billingsley

A senior-graduate level text and reference that links the disciplines of probability and measure theory. Including many practical problems and examples, it begins with an introduction to Borel's normal number theorem, proved by calculus alone, followed by short sections that establish the existence and fundamental properties of probability measures, including Lebesque measure on the unit interval. Coverage includes topics in measure, integration, random variables and expected values, convergence of distributions, derivatives and conditional probability, and stochastic processes.

Genres: Mathematics, Textbooks, Nonfiction

622 pages, Hardcover

First published January 1, 1979

Reviews

[Nour · Rating 3 out of 5]

in the general probability is somthing hard to understand , other thing the book was hard to read it , but it is interesting

[Tinwerume · Rating 4 out of 5]

Overall I'm quite happy with it, although then again I am comparing against Kallenberg so maybe my baseline is just skewed.

I also only read chapters 5 and 6 (convergence and conditionals), although I'd be surprised if earlier chapters were worse given the relatively easier material.

[Javier Burroni · Rating 5 out of 5]

Almost any book on formal probability ends up referring to this book at some point.
Therefore, it’s better to just begin with this one.
It is worth to mention that it’s contained

[Edith Z · Rating 5 out of 5]

Both concise and understandable (rare combination), really good examples, exercises were a bit challenging

[W · Rating 5 out of 5]

all-time classic, doesn't need the recommendation

[Steven Knox · Rating 2 out of 5]

This book succeeds at its apparent goal: be a single, self-contained work on measure-theoretic probability. Having worked through Billingsley's book, if someone asked me how to learn measure-theoretic probability my answer would be to work through a book on measure theory (say, Royden's Real Analysis) without probability, and then read Kolmogorov's seminal work Foundations of the Theory of Probability which applies measure theory to probability.

[Jerzy]

Browsing through, this seems fairly well-written -- but I should wait until I've picked up some more background in real analyis.

[Elmansouri]

i want to read it

[Mtaboga · Rating 4 out of 5]

Not an easy read, but contains many interesting results not found elswhere.